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"Why 0.618?" 》Quadratic equation of one variable PPT courseware 2
Do you know why the golden ratio is 0.618?
Can you provide multiple design options for a rectangular garden?
Can you make certain decisions based on product sales profits?
Like linear equations and fractional equations, quadratic equations are effective mathematical models of reality.
Observe the following equation:
10²+11²+12²＝13²+14²
Can you find five other consecutive integers such that the sum of the squares of the first three numbers is equal to the sum of the squares of the last two numbers?
1. The equation about x (k-3)x²+ 2x-1=0. When k≠3, it is a quadratic equation of one variable.
2. The equation about x (k²-1)x²+2(k-1)x+2k+2=0. When k≠±1, it is a quadratic equation of one variable. When k=-1, it is a linear equation of one variable.
Practice in class:
1． Once upon a time, a drunkard entered the house with a bamboo pole. He couldn't get in even if he held it horizontally or vertically. It was 4 feet wider than the door frame horizontally and 2 feet taller than the door frame vertically. Another drunkard taught him to follow the two opposite sides of the door. Holding the pole at an angle, the drunkard tried it and got in just right. Do you know how long the bamboo pole is? Please formulate an equation based on this problem.
2. Convert the equation (3x+2)²=4(x-3)² into the general form of a quadratic equation, and write down its quadratic term coefficients, linear term coefficients and constant terms.
What new knowledge did you learn in this lesson?
1. Learn what a quadratic equation is, its general form ax²+bx+c=0 (a, b, c are constants, a≠0) and related concepts, such as quadratic terms, linear terms, constant terms, and quadratic terms. Coefficient, linear term coefficient.
2. Be able to use quadratic equations to express quantitative relationships in real life.
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"Why 0.618?" 》Quadratic Equation PPT Courseware 3:
"Why 0.618?" 》Quadratic Equation PPT Courseware 3 As shown in Figure 2-8, a naval base is located at point A. There is an important target B 200 nautical miles due south of point A. There is an important target C 200 nautical miles due east of B. Small island D is located There is a supply dock on the island at the midpoint of AC;...
"Why 0.618?" 》Quadratic equation of one variable PPT courseware:
"Why 0.618?" 》Quadratic Equation PPT Courseware Learning Objective: How to get the golden ratio of 0.618. Further experience that equations are effective models for describing the real world. Be able to use equations to solve practical problems. Use mathematical beauty to decorate and beautify life. As shown in the figure...